To find the possible amounts of taffy and chocolate that Maya could buy, we need to first determine the total cost of each pair.
Let's use the equation: 9t + 12c = 30, where t is the pounds of taffy and c is the pounds of chocolate.
Let's solve for t in terms of c:
9t = 30 - 12c
t = (30 - 12c) / 9
t = (10 - 4c) / 3
Now, let's test out the given pairs to see which ones satisfy the equation:
1. Pair (0.5, 2.5):
t = (10 - 4(2.5)) / 3
t = (10 - 10) / 3
t = 0
9(0.5) + 12(2.5) = 4.5 + 30 = 34.5 (Does not equal 30)
2. Pair (1.5, 1.25):
t = (10 - 4(1.25)) / 3
t = (10 - 5) / 3
t = 5 / 3
9(1.5) + 12(1.25) = 13.5 + 15 = 28.5 (Does not equal 30)
3. Pair (2, 1):
t = (10 - 4(1)) / 3
t = (10 - 4) / 3
t = 6 / 3 = 2
9(2) + 12(1) = 18 + 12 = 30 (Is equal to 30)
4. Pair (1, 2):
t = (10 - 4(2)) / 3
t = (10 - 8) / 3
t = 2 / 3 = 1
9(1) + 12(2) = 9 + 24 = 33 (Does not equal 30)
Therefore, the only possible pair that represents the amounts of taffy and chocolate Maya could buy is (2, 1). Maya could buy 2 pounds of saltwater taffy and 1 pound of chocolate.
Maya is visiting her favorite candy store, the Sugar Spoon. The candy there is in self-serve bins, so Maya can pick out exactly the amount she wants. She has $30 to spend, and she wants to get a combination of saltwater taffy that costs $9 per pound and chocolate that costs $12 per pound. Which pairs (t,c) represent possible amounts of taffy and chocolate, in pounds, that Maya could buy?
0.5,2.5
1.5,1.25
2,1
1,2
1 answer
1 answer